Figs. 1 and 2 show the lines of electric force in the space surrounding two charged spheres. Fig. 1 shows the case where the charges are opposite, fig. 2 the case where they are similar. In fig. 1 the attraction between the spheres may be thought of as due to the tendency of the lines of force to shorten themselves. Similarly, the mutual repulsion of the spheres in fig. 2 may be regarded as a consequence of the mutual repulsion of the lines of force.
The distribution of a charge upon an insulated conductor isolated in space depends upon the shape of the conductor. If the conductor is spherical, the charge is uniformly distributed. If the curvature varies from point to point, the quantity of charge per unit area, or the electric surface density, will vary from point to point. The sharper the curvature is, the greater the surface density will be. In fig. 3 the distance of the dotted lines from the surface of the conductors is proportional to the surface density. These lines, therefore, give a graphical representation of the distribution of charge. In sharply pointed conductors nearly the whole charge will be concentrated at the pointed end. Owing to
the large charge per unit area at the pointed part, particles of dust, water-vapour, &c., will be powerfully attracted, will become charged by conduction, and will then be powerfully repelled. In this way the original charge will be rapidly dissipated. This effect may be shown by keeping a sharply pointed conductor powerfully charged by an electric machine. The streaming of the particles from the point produces a wind which is sufficient to blow out the flame of a candle.
Conductors which are intended to retain their charge for a long period must be smooth and polished, and the maximum curvature must be as small as possible. In lightning-conductors practical advantage is taken of this 'power of points' to dissipate a charge rapidly.
The distribution of the charge on a conductor is influenced by the presence of other conductors, whether charged or not. This is due to what is called electrostatic induction. If an uncharged insulated conductor B is brought near a charged conductor A, a charge of the opposite kind is induced on the parts of B nearer to A, and a charge of the same kind on the parts farther away from A. Since B was originally uncharged, these induced charges are equal in amount.
If B is now removed to a distance, the induced charges neutralize one another, and B returns to its original uncharged state.
While B is near A, let the induced charge of the same kind as the charge on A be neutralized by touching B with an earth-connected conductor, say the finger. On removing B to a distance, it will no longer be uncharged as before, but will have a charge of the opposite kind from that on A. B is now said to have been charged by induction.